Question

hovering mosquito is hit by a raindrop that is 45 times as massive and falling at 8.1 m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic? Express your answer with the appropriate units.

Answer 1

7.92 m/s

Step-by-step explanation:

`m_1` = Mass of raindrop =
`45m_2`

`m_2` = Mass of mosquito

`u_1` = Initial Velocity of raindrop = 8.1 m/s

`u_2` = Initial Velocity of mosquito = 0 m/s

`v` = Velocity of center of mass

For elastic collision

`m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow v=(m_1u_1 + m_2u_2)/(m_1 + m_2)\\\Rightarrow v=(45m_2* 8.1 + m_2* 0)/(45m_2 + m_2)\\\Rightarrow v=(364.5m_2)/(46m_2)\\\Rightarrow v=7.92\ m/s`

Hence, the velocity of the attached mosquito, falling immediately afterward is 7.92 m/s